Question

For a particular brand of tube lights , it is known that the mean operating life of the tubes is 1,200 hours with a standard deviation of 210 hours. What is the probability that the mean for a random sample of size 100 will be between 1140 and 1260 hours?

Answer 1

Solution :

Given that,

mean = = 1200

standard deviation = = 210

n = 100

= 1200

= / n = 210 / 100 = 21

P(1140 < < 1260 )  

= P[(1140 - 1200) / 21 < ( - ) / < (1260 - 1200) / 21 )]

= P( - 2.86 < Z < 2.86)

= P(Z < 2.86) - P(Z < - 2.86)

Using z table,  

= 0.9979 - 0.0021

= 0.9957